Electromagnetic Signal of a Proton Beam in Biological Tissues for a Potential Range-Verification Approach in Proton Therapy

Abstract

In the present work we investigate the fundamental properties of a proton beam's electromagnetic signal as a candidate for range verification in proton therapy. We compute the electric and magnetic fields from a pulsed proton beam in biological tissues in a cylindrical geometry via a dedicated analytical solution of the Maxwell equations. The tissues are specified through their dielectric response and stopping power, where we consider a straight trajectory with a range that corresponds to protons with an initial energy of 150 MeV. We analyze the characteristics of the pulse and the impact of the pulse shape. The effect of the tissue's conductivity on the deposited charges is specifically taken into account. In addition, we calculate and analyze the radiative pulse through the Li\'enard-Wiechert approach. We find that the conductivity charge relaxation has a big influence on the electric field strength, even in the presence of boundaries. It strongly depends on its environment, i.e., the permittivity, conductivity, and boundaries of the surrounding tissues. The electric field that originates from the primary protons vanishes in a time scale of ns. Conversely, the magnetic field is independent of its environment and constant in strength during a rectangular pulse ($10\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$). For $\ensuremath{\mu}\mathrm{A}$ peak beam currents it lies in the pT range, 10 cm away from the beam axis, and is therefore detectable through, e.g., optical magnetometry. Its spatial profile, however, does not exhibit a distinct feature with respect to the range, but decreases rather smoothly and characteristically along the beam axis. The typical velocity dependence of the magnetic field strength is suppressed, due to the increasing charge density downstream. Finally, the primary protons give rise to an electromagnetic pulse in the radio spectrum (it peaks at approximately 9 GHz). It originates spherically around the range and consists partially of bremsstrahlung and Cherenkov radiation. Yet, a broader comparison to other radiation sources, e.g., secondary electron bremsstrahlung, is required. Based on our findings, we conclude that the magnetic field signal has favorable properties that motivate its detection experimentally for range-verification purposes.